5.9 - Centre of Mass

Centre of gravity

• The centre of gravity of an object is the point through which its entire weight can be considered to act.
• Because the whole weight acts at this point, it's also the point where the object's mass can be thought of as concentrated.
• For a regular, symmetrical shape, the centre of gravity is at its geometric centre (e.g. the centre of a uniform sphere), while an irregular shape has one too, even though symmetry can't be used to find it.

Finding the centre of gravity by suspension

• When an object is hung so it can swing freely, it comes to rest with its centre of gravity vertically below the point of suspension.
• If its centre of gravity is not directly below the pivot, the weight acts at a perpendicular distance from that point, producing a moment that turns the object until the weight acts in line with the pivot.

Locating the centre of gravity of a flat shape

This is used to find the centre of gravity of a flat shape (a plane lamina):

1. Suspend the shape from a pivot so it can swing freely, and hang a plumb line from the same point. Wait until both stop moving.
2. Draw a line on the shape along the plumb line.
3. Repeat with the shape suspended from a different pivot point, drawing a second line.
4. The centre of gravity is where the lines cross.

Stability - Centre of gravity and base area

An object is stable (harder to tip over) when it has a low centre of gravity and a wide base area.

Why it depends on moments

The point where the object touches the ground acts as a pivot. When the object is tilted:

• While the centre of gravity stays over the base, the weight produces a moment that turns the object back down onto its base.
• If tilted far enough that the centre of gravity passes outside the edge of the base, the weight produces a moment that turns it the other way, and it topples.

A low centre of gravity and wide base mean the object can be tilted much further before its centre of gravity passes the edge of the base.